Problem: Reduce to lowest terms: $- \dfrac{6}{5} \div \dfrac{4}{3} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{4}{3}$ is $ \dfrac{3}{4}$ Therefore: $ - \dfrac{6}{5} \div \dfrac{4}{3} = - \dfrac{6}{5} \times \dfrac{3}{4} $ $ \phantom{- \dfrac{6}{5} \times \dfrac{3}{4}} = \dfrac{-6 \times 3}{5 \times 4} $ $ \phantom{- \dfrac{6}{5} \times \dfrac{3}{4}} = \dfrac{-18}{20} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-18}{20} = \dfrac{-18 \div 2}{20 \div 2} = -\dfrac{9}{10} $